** Next:** Acknowledgements

### Abstract:

From a description of one of the simplest models of computation
(discrete, finite state automata), a complex dynamical system is formed.
Known as a cellular automaton, it has been proved that these systems can
harbor the conditions necessary for universal computation. An
exploration is made into the dynamics of cellular automata in order to
answer the question: is their a deep connection between the theories of
dynamical systems and computation? Is there an analog for the notion of
universal computation in dynamical systems theory? The thermodynamic
notion of a phase-transition is proposed as the model in which
computation and dynamics commingle. Christopher Langton's thesis,
*Chaos at the Edge of Computation*, represents the culmination of
the ideas presented within.

# Computation, Dynamics and the Phase-Transition

**Jeremy Avnet**

*jeremy (at) theory.org*

*Date:* 6th June 2000

Key words and phrases: Cellular automata, complexity, computability, computation, decidability, dynamical systems,
Halting Problem, phase-transition, Wolfram classes

** Next:** Acknowledgements
Jeremy Avnet (brainsik); Senior Thesis, Mathematics; University California, Santa Cruz; 6th June 2000; email: jeremy (at) theory.org